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Harmonic approximation and its applications

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Approximation, Complex Analysis, and Potential Theory

Part of the book series: NATO Science Series ((NAII,volume 37))

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Abstract

These lectures survey some recent developments concerning the theory and applications of harmonic approximation in Euclidean space. We begin with a discussion of the significance of the concept of thinness for harmonic approximation, and present a complete description of the closed (possibly unbounded) sets on which uniform harmonic approximation is possible. Next we demonstrate the power of such results by describing their use to solve an old problem concerning the Dirichlet problem for unbounded regions. The third lecture characterizes the functions on a given set which can be approximated by harmonic functions on a fixed open superset. Finally, we return to applications, and explain how some problems concerning the boundary behaviour of harmonic functions have recently been solved using harmonic approximation.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University College Dublin, 4 Dublin, Ireland

    Stephen J. Gardiner

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  1. Stephen J. Gardiner
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Editors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Armenia, Yerevan, Armenia

    N. Arakelian

  2. Département de Mathématiques et de Statistique, Université de Montréal, Montréal, Québec, Canada

    P. M. Gauthier  & G. Sabidussi  & 

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© 2001 Springer Science+Business Media Dordrecht

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Gardiner, S.J. (2001). Harmonic approximation and its applications. In: Arakelian, N., Gauthier, P.M., Sabidussi, G. (eds) Approximation, Complex Analysis, and Potential Theory. NATO Science Series, vol 37. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0979-9_7

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  • DOI: https://doi.org/10.1007/978-94-010-0979-9_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-0029-4

  • Online ISBN: 978-94-010-0979-9

  • eBook Packages: Springer Book Archive

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